A GEAR DOOR WARNING ON DEP HANDLED BY CREW; COORDINATED WITH MAINT AND DISPATCH DRAWAS COMPLAINT FROM ATC ON ARR BECAUSE AN EMER WAS NOT DECLARED.

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DEPARTED COS AND SHORTLY AFTER RETRACTING THE GEAR; NOTICED A YELLOW GEAR DOOR OPEN LIGHT AND A RED R MAIN GEAR LIGHT. LEVELED AT 10000 FT AND ASKED FOR A HDG WHILE WE COMPLETED THE PROC AND TALKED TO MAINT AND DISPATCH. COMPLETED THE QRH PROC BY SLOWING AND THEN CYCLING THE GEAR. ON RETRACTION; THERE WAS NO CHANGE IN THE LIGHTS. DISCUSSED SIT WITH MAINT AND DISPATCH. MAINT AGREED THERE WAS NOTHING FURTHER TO DO. AIRPLANE FLEW NORMALLY WITH THE EXCEPTION OF SLIGHTLY REDUCED CLB RATE. AFTER SOME DISCUSSION; DISPATCH AGREED THAT WE COULD CONTINUE TO STL BY MOVING OUR ALTERNATE CLOSER TO BELLEVILLE AND RECHK FUEL AT GARDEN CITY AND SALINA. IF A FUEL STOP WAS NECESSARY; WE COULD LAND AT MCI. BOTH CHKS INDICATED THAT THE FUEL BURN WAS ONLY SLIGHTLY HIGHER THAN NORMAL. PLANNED TO ARRIVE OVER BUM WITH A MINIMUM OF APPROX 10000 LBS. ARRIVED BUM WITHIN EXCESS OF 13000 LBS. WX AT STL AND BLV OK WAS. BRIEFED FLT ATTENDANTS AND PAX AND DID NOT DECLARE AN EMER. HOWEVER; WE DID ASK FOR THE EMER EQUIP AS A PRECAUTION IN STL. WHEN ON STL APCH FREQ; WE ASKED THEM TO ADVISE THE TWR THAT WHILE WE ANTICIPATED A NORMAL LNDG; IF THE GEAR DOOR REMAINED OPEN; WE MAY NEED TO STOP N THE RWY (ACCORDING TO PROC) TO HAVE MAINT RAISE THE DOOR. REQUESTED AN ILS TO RWY 30L. EXTENDED THE GEAR AT 3500 FT AND HAD ALL NORMAL INDICATIONS. ADVISED THE TWR THAT THE LNDG AND TURNOFF WOULD BE NORMAL. AFTER A NORMAL LNDG; WE CHANGED TO GND CTL. THE CTLR REQUESTED WE CALL THE TWR AFTER LNDG; WHICH WE DID. AFTER SOME CLARIFICATION OF WHAT WE HAD REQUESTED; THE SUPVR SUGGESTED THAT IN THE FUTURE IT WOULD BE BETTER TO DECLARE AN EMER TO FACILITATE TFC FLOW AND EMER EQUIP. ALSO; HE HAD NOT HEARD THE FO TELL THE CTLR (ON FINAL) THAT THE LNDG AND TURNOFF WOULD BE NORMAL.